v1.0 5may2000: First version
Taken from Dr Neil Johnson's lecture notes for Chaos (MPhys part B/physics/ox.ac.uk).
What is this page for?
We had the following table in a lecture today and I thought it was such a fanatastic way of classifying phenomena and systems according to their dynamical properties that it just had to go online.
Thought: It would be pretty cool to make this into a physics/systems resource. I might start collecting links here.
What is linearity?
A system may be described by a bunch of equations, expressed in terms of a load of independent variables (independent variables describe different unconnected things). If the independent variables are related to one another such that there aren't any squares or cubes or higher powers, the system is said to be linear. A property of linearity is that you can add valid solutions and come up with another valid solution, which is why it's so neat and easy.
Nonlinearity is when the above doesn't apply, like position depending on the sine of velocity. It's tougher.
The table
The inset parts of the table are what Dr Johnson labelled as beyond the frontier. They're things we don't know about, can't solve, and are generally really tough (they're also generally the coolest). Chaos lies on the cust of complexity, but is not the same as randomness: The only true randomness known comes in quantum mechanics.
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Number of variables |
Linear |
Nonlinear |
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n = 1 |
Growth, decay, or equilibrium
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n = 2 |
Oscillations
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n >= 3 |
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Chaos
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n » 1 |
Collective phenomena
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Continuum |
Waves and patterns
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Spatio-temporal complexity
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